Frequency Synchronization in Distributed Antenna Systems: Pairing-Based Multi-CFO Estimation, Theoretical Analysis, and Optimal Pairing Scheme

In this paper, we consider the frequency synchronization issue in orthogonal frequency division multiplexing distributed antenna systems. There may exist multiple carrier frequency offsets (CFOs) between the transmitter and distributed receive antennas. To solve the multi-CFO estimation problem, we first derive the blind maximum likelihood estimator, which has superior estimation performance, but exhibits high computational complexity. Furthermore, we develop a blind pairing-based efficient estimator (PBEE), which divides the multiple antennas into pairs of two. The two CFOs in each pair are jointly estimated with a carefully designed cost function, which proves to be exactly a cosine function parameterized by the two CFOs even with the effect of noise. Consequently, the joint estimation of the two CFOs can be simplified to the one-dimensional search optimization problem. The PBEE can achieve better CFO estimation performance than the existing competitors. From the theoretical mean square error (MSE) analysis of PBEE, we further derive the optimal antenna pairing scheme by minimizing the signal-to-noise ratio degradation caused by the uncompensated residual CFOs. Finally, the Cramér-Rao bound of CFO estimation is derived and numerical results are provided to corroborate the proposed studies.